1. Field of the Invention
The present invention relates to a depolarizer, a spectroscope, and a polychromater.
2. Description of the Related Art
In general, a dispersion device which is used in a spectroscope has polarization dependence. Accordingly, when such a light polarized in a particular direction, as a linearly polarized light, is incident on the dispersion device, even though the incident light has the same energy, the dispersion device has a particular output characteristic in accordance with the direction in which the incident light is polarized. A diffraction grating is a representative example of the dispersion device. The diffraction grating has the polarization dependence that the diffraction efficiency varies with a polarization state of the incident light. In other words, a reflectance with the polarized light component perpendicular to a groove cut in the diffraction grating and a reflectance with the polarized light component parallel to the grove are different from each other. Therefore, because the diffraction efficiency varies according to the polarization state of the incident lights in the spectroscope using the diffraction grating, a trouble occurs on measuring a spectroscopic characteristic of the incident light. In order to remove such a polarization dependence, it is necessary to provide a polarization scrambler which converts the incident light having the arbitrary polarization state, into a circular polarized light or no polarized light.
A depolarizer is used as the polarization scrambler. An example of a depolarizer according to a prior art, for example, as disclosed in Japanese Patent No. 2,995,985, will be explained with reference to FIGS. 7A and 7B. A reference numeral 2 denotes a depolarizer which is composed of crystal plates 2A and 2B. The crystal plate 2A has a thickness which continuously changes in a direction of 45 degree with an optical axis 21 thereof, as shown in FIG. 7A. The crystal plate 2B has a thickness which continuously changes in a direction of −45 degree with an optical axis thereof. The depolarizer 2 is constituted by sticking the crystal plates 2A and the crystal plate 2B so that the optical axis 21 and the optical axis 22 intersect orthogonally with each other, as shown in FIG. 7B.
As well known in the art, a crystal has an optical axis extending to a particular direction on the basis of a crystalline structure. When a light enters the crystal, the light is separated to a plane light parallel to the optical axis and a plane light perpendicular to the optical axis. Then, the plane lights travel in the crystal at phase speeds which are different from each other. This phenomenon will be called a birefringence. In other words, the crystal has the birefringence which causes a phase difference between a light component oscillating in a direction parallel to the optical axis and a light component oscillating in a direction perpendicular to the optical axis, of the light which passes through the crystal. The phase difference caused in the crystal is proportional to the thickness of the crystal. Because the thickness of each of the crystal plates 2A and 2B varies continuously, the thickness of each of the crystal plates 2A and 2B is different to a point which the light passes.
More particularly, even though the polarization states of lights L11, L12, and L13 shown in FIG. 7B are equal to one another before the lights L11, L12, and L13 pass through the crystal plates 2A and 2B, because the phase differences which are caused to the lights L11, L12, and L13 in the crystal plates 2A and 2B are different from one another, the polarization states of the lights L11, L12, and L13 are different from one another after the lights L11, L12, and L13 pass through the crystal plates 2A and 2B. Accordingly, it is possible that the depolarizer 2 converts the polarization state of the light to the state wherein a large number of polarization states are mixed with respect to a space. In other words, the depolarizer 2 disturbs the polarization states of the lights with respect to a space. However, the depolarizer 2 does not have an effect with respect to the incident light which oscillates in the direction parallel or perpendicular to the optical axis 21 or 22. As a result, such an incident light passes through the depolarizer 2 with keeping the polarization state before the incident light enters the depolarizer 2.
FIG. 8 is a view showing a configuration of spectroscope which uses the depolarizer 2. In FIG. 8, a reference numeral 3 denotes an incident slit. A reference numeral 4 denotes a concave mirror. A reference numeral 5 denotes a diffraction grating. A reference numeral 6 denotes a concave mirror. A reference numeral 7 represents an outgoing slit. The light which passes through the incident slit 3 is diffracted with a different angle by the diffraction grating 5 on the basis of the wavelength of the light. The angle of the diffraction grating 5 determines the wavelength component of the light that passes through the outgoing slit 7 and reaches the light receiving unit 8A. In other words, it is possible to sweep the wavelength component of the light and to obtain a spectrum of the light by rotating the diffraction grating 5 towards a rotational direction. The depolarizer 2 is positioned after the incident slit 3 so as to direct the optical axis thereof in a direction of 45 degree with grooves of the diffraction grating 5.
The depolarizer 2 makes the incident light have the state wherein a large number of polarization states are mixed. When the incident light oscillating in the direction parallel or perpendicular to the optical axis of the depolarizer 2, is incident on the depolarizer 2, the incident light passes through the depolarizer 2 with keeping the polarization state before the light enters the depolarizer 2. After the incident light passes through the depolarizer 2, the incident light enters the diffraction grating 5 with the angle of 45 degree with the grooves of the diffraction grating 5. Therefore, even though the incident light is incident on the depolarizer 2 in any the polarization state, the incident light is incident on the diffraction grating 5 in an always constant ratio between the light component oscillating in the direction perpendicular to the grooves of the diffraction grating 5 and the light component oscillating in the direction parallel to the grooves of the diffraction grating 5. As a result, diffraction efficiency does not vary in the spectroscope according to the polarization state of the incident light.
By the way, because the optical axis 21 of the crystal plate 2A and the optical axis 22 of the crystal plate 2B intersect orthogonally with each other in the above-mentioned conventional depolarizer 2, the light which is parallel to the optical axis 21 of the crystal plate 2A is perpendicular to the optical axis 22 of crystal plate 2B. Therefore, because refractive indexes are different from each other at both sides of the inclined surface between the crystal plates 2A and 2B, the light is refracted on the inclined surface. Furthermore, a refraction angle to the light component oscillating in the direction parallel to the optical axis 21 of the crystal sheet 2A and a refraction angle to the light component oscillating in the direction perpendicular to the optical axis 21 of the crystal plate 2A are different from each other. More specifically, a light component of an incident light I11 shown in FIG. 9, oscillating in the direction parallel to the optical axis 21 becomes a refracted light R11. Further, a light component of the incident light I11, oscillating in the direction perpendicular to the optical axis 21 becomes a refracted light R12. In other words, there is a problem in which the incident light is separated into two light rays along the direction of the inclined surface in depolarizer 2.
Accordingly, in also the spectroscope shown in FIG. 8, the light is separated into two light rays in the depolarizer 2. As a result, two focal point positions are formed on the outgoing slit 7. FIGS. 10A and 10B are front views of the outgoing slit 7 shown in FIG. 8. In FIG. 10A, a reference mark F12 denotes a focal point position in case the depolarizer 2 is not provided in the spectroscope. Reference marks F11 and F13 denote focal point positions in case the depolarizer 2 is provided in the spectroscope.
Power of each of the light ray which has the focal point position F11 and the light ray which has the focal point position F13 varies according to the polarization state of the incident light. Using Jones vector notation representative of the polarization state of the light, it is possible to express an incident light E0 having an arbitrary completely polarization state as shown in Equation (1). A first component of Equation (1) represents a scalar value of an X directional component, and a second component of Equation (1) represents a scalar value of a Y directional component. In Equation (1), “f” represents a frequency, “δ” represents an initial phase, “δ” represents a phase difference between the X directional component and the Y directional component, and “φ” represents an azimuth angle.
                              E          0                =                              1                          2                                ⁢                      (                                                                                cos                    ⁢                                                                                  ⁢                    ϕ                                                                                                              -                      sin                                        ⁢                                                                                  ⁢                    ϕ                                                                                                                    sin                    ⁢                                                                                  ⁢                    ϕ                                                                                        cos                    ⁢                                                                                  ⁢                    ϕ                                                                        )                    ⁢                      (                                                                                exp                    ⁡                                          (                                                                                                    -                            ⅈ                                                    ⁢                                                                                                          ⁢                          δ                                                2                                            )                                                                                                                                        exp                    ⁡                                          (                                              δ                        2                                            )                                                                                            )                    ⁢                      exp            ⁡                          [                              ⅈ                ⁡                                  (                                                            2                      ⁢                      π                      ⁢                                                                                          ⁢                      f                      ⁢                                                                                          ⁢                      t                                        -                                          δ                      0                                                        )                                            ]                                                          (        1        )            
When incident light represented by Equation (1) passes through the depolarizer 2, the incident light is separated into two light rays R11 and R12. Then, the light rays R11 and R12 which have passed through the diffraction grating 5 come into two focal points F11 and F13 on the outgoing slit 7 as shown in FIG. 10B, respectively.
In FIG. 10B, “E1” of Equation (2) represents the state of the light ray at the focal point F11, and “P1” of Equation (3) represents the power of the light ray at the focal point F11. “E2” of Equation (4) represents the state of the light ray at the focal point F13, and “P2” of Equation (5) represents the power of the light ray at the focal point F13. “Pθ” of Equation (6) represents a partial polarizer of the azimuth angle θ. “G” of Equation (7) represents a diffraction grating whose diffractive efficiency of the X directional component is equal to a and whose diffraction efficiency of the Y directional component is equal to β. “*” represents a complex conjugate in each of Equations (3) and (5). As readily understood from Equation (8), a total intensity of the light rays at two focal points F11 and F13 is a constant regardless of the state of the incident light E0. However, as readily understood from Equations (3) and (5), an intensity ratio between the light ray at the focal point F11 and the light ray at the focal point F13 varies in accordance with the state of the incident light E0.
                              E          1                =                              G            ·                          P                              45                ∘                                      ·                          E              0                                =                                    1                              2                                      ⁢                          (                                                cos                  ⁢                                                                          ⁢                                      ϕ                    ·                    cos                                    ⁢                                      δ                    2                                                  -                                                      ⅈ                    ·                    sin                                    ⁢                                                                          ⁢                                      ϕ                    ·                    sin                                    ⁢                                      δ                    2                                                              )                        ⁢                          (                                                                    α                                                                                        β                                                              )                        ⁢                          exp              ⁡                              [                                  ⅈ                  ⁡                                      (                                                                  2                        ⁢                        π                        ⁢                                                                                                  ⁢                        f                        ⁢                                                                                                  ⁢                        t                                            -                                              δ                        0                                                              )                                                  ]                                                                        (        2        )                                          P          1                =                                            E              1                        ·                          E              1              *                                =                                    1              2                        ⁢                          (                                                                                          cos                      ⁢                                                                                                            2                                    ⁢                                      ϕ                    ·                                          cos                      2                                                        ⁢                                      δ                    2                                                  +                                                      sin                    2                                    ⁢                                                                          ⁢                                      ϕ                    ·                                          sin                      2                                                        ⁢                                      δ                    2                                                              )                        ⁢                          (                                                α                  2                                +                                  β                  2                                            )                                                          (        3        )                                          E          2                =                              G            ·                          P                              -                                  45                  ∘                                                      ·                          E              0                                =                                    1                              2                                      ⁢                          (                                                sin                  ⁢                                                                          ⁢                                      ϕ                    ·                    cos                                    ⁢                                      δ                    2                                                  +                                                      ⅈ                    ·                    cos                                    ⁢                                                                          ⁢                                      ϕ                    ·                    sin                                    ⁢                                      δ                    2                                                              )                        ⁢                          (                                                                                          -                      α                                                                                                            β                                                              )                        ⁢                          exp              ⁡                              [                                  ⅈ                  ⁡                                      (                                                                  2                        ⁢                        π                        ⁢                                                                                                  ⁢                        f                        ⁢                                                                                                  ⁢                        t                                            -                                              δ                        0                                                              )                                                  ]                                                                        (        4        )                                          P          2                =                                            E              2                        ·                          E              2              *                                =                                    1              2                        ⁢                          (                                                                                          sin                      ⁢                                                                                                            2                                    ⁢                                      ϕ                    ·                                          cos                      2                                                        ⁢                                      δ                    2                                                  +                                                      cos                    2                                    ⁢                                                                          ⁢                                      ϕ                    ·                                          sin                      2                                                        ⁢                                      δ                    2                                                              )                        ⁢                          (                                                α                  2                                +                                  β                  2                                            )                                                          (        5        )                                          P          θ                =                  (                                                                                          cos                    2                                    ⁢                  θ                                                                              cos                  ⁢                                                                          ⁢                                      θ                    ·                    sin                                    ⁢                                                                          ⁢                  θ                                                                                                      cos                  ⁢                                                                          ⁢                                      θ                    ·                    sin                                    ⁢                                                                          ⁢                  θ                                                                                                  sin                    2                                    ⁢                                                                          ⁢                  θ                                                              )                                    (        6        )                                G        =                  (                                                    α                                            0                                                                    0                                            β                                              )                                    (        7        )                                P        =                                            P              1                        +                          P              2                                =                                    1              2                        ⁢                          (                                                α                  2                                +                                  β                  2                                            )                                                          (        8        )            
In the spectroscope shown in FIG. 8, the two light rays into which the light passing through the depolarizer 2 is separated, is reflected by the concave mirror 4 and is diffracted by the diffraction grating 5. Equation (9) represents a relationship between an incident angle and a diffraction angle of the diffraction grating 5. In Equation (9), “m” represents the diffraction order, “d” represents a grating constant of the diffraction grating 5, “λ” represents a wavelength of the light, “ξ” represents an angle between the incident light and a surface perpendicular to grating grooves of the diffraction grating 5. “Ψ1” represents an incident angle of the incident light on the diffraction grating 5, and “Ψ2” represents a diffraction angle of the diffracted light by the diffraction grating 5.mλ=d cos ξ(sin ψ1+sin ψ2)  (9)
FIG. 11 is a view showing a relationship of the angle ξ, the incident angle Ψ1, and the diffraction angle Ψ2. Under restriction of positions of the parts, there is a case that the light is reflected with deviating from an axis of the concave mirror 4, and inputted to the diffraction grating 5 so as to be inclined in the Y axis direction. More particularly, in an eight stages spectroscope disclosed in Japanese Patent Application No. 2001-335385, the refracted lights R11 and R12 are inclined on the diffraction grating 5 with same incident angles Ψ1 with each other but the different diffraction angles ξ. Therefore, as readily understood from Equation (9), Because two light rays R11 and R12 are outputted from the diffraction grating 5 with diffractive angles Ψ2 different from each other, there occurs displacement in two light rays R11 and R12 in the X axis direction shown in FIG. 8. As a result, as shown in FIG. 10B, two focal points F11 and F13 are formed in a slanting direction with the cutting direction of the outgoing slit 7. In other words, focal points F11 and F13 are provided at the different positions in the direction perpendicular to the cutting direction of the outgoing slit 7.
As described above, if the focal points F11 and F13 are provided at the different positions in the direction perpendicular to the cutting direction of the outgoing slit 7, and as explained with reference to Equations (3) and (5), the intensity ratio between the light rays at the two focal points F11 and F13 varies in accordance with the state of the incident light, the spectroscope outputs a measured central wavelength which is different from a true central wavelength.
FIGS. 12A to 12C are views showing spectrum waveforms which are outputted to a spectrum display unit 10 shown in FIG. 8. FIG. 12A is a view showing a measured spectrum in case the light is not separated, and one focal point is formed on the outgoing slit 7. FIG. 12B is a view showing a measured spectrum in case the intensity ratio between the light rays at two focal points F11 and F13 shown in FIG. 10B is equal to 1:0. FIG. 12C is a view showing a measured spectrum in case the intensity ratio between the light rays at the two focal points F11 and F13 shown in FIG. 10B is equal to 0:1. In FIGS. 12A to 12C, “λ0” represents the true central wavelength of the incident light, and “Δλ” represents a difference between the true central wavelength and the measured central wavelength. The measured spectrum obtained by the spectroscope using the depolarizer 2 varies from the state shown in FIG. 12B to the state shown in FIG. 12C, in accordance with the polarization state of the light. As a result, it is difficult to measure the true central wavelength.
If any one of the powers of the light rays at two focal points F11 and F13 of the outgoing slit 7 shown in FIG. 10B, concerning the incident light in the arbitrary polarization state is always equal to zero, and the other of the powers is always constant, it is possible to obtain the spectrum having a stable central wave length concerning the arbitrary polarization state. For example, if it is possible to always obtain the state shown in FIG. 12A, it is possible to measure the spectrum having the true central wavelength.
In addition, although there are a depolarizer and a spectroscope which is disclosed in Japanese Patent Application No. 2001-196745 and which obtain a spectrum having a stable central wavelength concerning the incident light in the arbitrary polarization state, the depolarizer and a spectroscope can only use in case the diffraction efficiency α in the X directional component and the diffraction efficiency β in the Y directional component of a spectroscopic diffraction grating which is used in the spectroscope are equal to α=1 and β=0 or α=0 and β=1.